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C₂²⋊#66343 #13047072

• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

211 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^4,3^4|a^2=c,e^3=h,f^3=g,b^a=bd,e^a=efg^2,f^a=ef^2g^2,g^a=g^2h,h^a=gh,e^c=e^2h^2,f^c=f^2g^2,g^c=g^2,h^c=h^2

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 790);